In the medical field, the diagnosis using a tomographic image obtained through CT (Computed Tomography) or MRI (Magnetic Resonance Imaging) is commonly performed. With the development of computer hardware technology in recent years, it becomes easy to generate a 3-dimensional image from a tomographic image, and exact and objective grasping of a position and configuration of the affected part is possible. In addition, recently, many researches on a cutting of a splinter of bone, a synthetic simulation and a distance measurement of a skin incision part have been carried out by using the 3-dimensional image.
In the field of dentistry, the CT for medical use has so far been diverted, but it cannot be said that the CT for medical use is optimal for dentistry, from the standpoints of the device scale, the resolution of the image and so on.
To resolve the problem, a 3DX Multi Image Micro CT (which is hereinafter called 3DX device) has been developed by Arai Y et al in the radiology group of the department of dentistry of the Nihon University. See the following documents.                Arai Y, Honda K, Iwai K et al: “Practical Model “3DX” of Limited Cone-Beam X-ray CT for Dental Use”, CARS2001, 2001, pp. 671-675.        “Basic Performance of Practical Model “3DX Multi Image Micro CT” of Limited Cone-Beam X-ray CT”, Dental Radiology 2000, 40(2), 2000, pp. 145-154.        
The photographic area of the 3DX device can be local and the 3DX device itself is configured to reduce the quantity of X-ray radiation as low as possible, and the X-ray exposed dose is reduced with the whole 3DX device.
The range of optical density in the photography area is quantized so that it may be expressed by 256 gradation levels. When compared with the conventional CT data, the 3-dimensional projection data obtained by using the 3DX device have high resolution. It is possible to display a 3-dimensional tomographic image from an arbitrary direction. Detailed observation of a hard tissue of a jawbone or an internal ear which was conventionally difficult to be carried out is also possible. Thereby, the effectiveness in the hard tissue diagnosis in the fields of otolaryngology and dentistry is confirmed.
By using the 3DX device, the present inventors have developed an image processing method which generates a tomographic image by developing a 3-dimensional projection data, obtained by the 3DX device, on two-dimensional images in multiple directions around the Z-axis (or the perpendicular line passing through the center of an object). After performing noise reduction and outline extraction of an object on the tomographic image, this image processing method performs rearrangement of the projection data in the 3-dimensional space. This technique takes into account the fact that the data obtained from the 3DX device are voxel data in the 3-dimensional space.
Next, the outline of the processing will be explained using FIG. 1.
(Extraction of Images)
First, the 3DX device shown in FIG. 1(A) is used to obtain the 3-dimensional projection data as shown in FIG. 1(B), and two-dimensional images are extracted in the multiple directions around the Z-axis from the 3-dimensional projection data as shown in FIG. 1(C). Extraction of images is the reverse algorithm to the method of generating a tomographic image. This extraction is not simply performed at intervals of 0.125 (one voxel) which are the spatial resolution, but the moving-average processing is performed in order to include the noise reduction processing, and the images are extracted so that each image becomes a single image with the average value of eight images in the depth direction of the extraction.
(2-Dimensional Image Processing)
Next, noises are removed from the obtained original images. Since it is difficult to extract the object correctly by the simple binarization processing, the following processing which will be described below is performed and binarized outline images are obtained (FIG. 1(D)).    (1) Contrast adjustment by density conversion    (2) Outline detection using the Gaussian filter    (3) Binarization    (4) Outline extraction by skipping processing(Reconstruction of 3-Dimensional Image)
The obtained outline images are rearranged in the 3-dimensional space for each of the respective directions in the reverse order of the directions in which the images are extracted in the 2-dimensional space, and the 3-dimensional image created for every direction is compounded in the 3-dimensional space (FIG. 1(E)).
At this time, the object areas extracted for the respective directions are different, and the outline information on the missing object can also be interpolated from the image data processed for the other directions.
(Multi-Axial Extraction)
Apart from the manner in which two-dimensional images are extracted in the directions around the Z-axis from the 3-dimensional projection data as shown in FIG. 1(C), there is another method of extraction of two-dimensional images. Namely, two-dimensional images may be extracted along the axes of the lines connecting together the center of each side of one of regular polyhedrons, including a regular tetrahedron (A), a regular hexahedron (B), a regular octahedron (C), a regular dodecahedron (D) and a regular icosahedron (E), shown in FIG. 2, and the center of the one of regular polyhedrons.
It has been confirmed until now that the diagnostic imaging of 5000 cases is performed using the 3DX device and they are effective.
On the other hand, the diagnosis using a 3-dimensional image is demanded for the advancement of dental treatment. The image obtained from the 3DX device has several noises because of its high resolution, and the binarization processing generally used for extraction of a bone area may result in a missing of the object surface and it was very difficult to obtain a 3-dimensional image with good quality of image. As the technique of restoring the missing or cut-off outline, there have been several methods are proposed, such as the method of interpolating the outline smoothly using the curvature of a lacking part or a dispersed point, the method of detecting the outline based on the human vision structure and subjective evaluation, and the interpolation method using the Hough transform. In the field of dentistry, the method of generating a traced drawing based on optimization has been reported.
In addition, Japanese Laid-Open Patent Application No. 2003-061956 discloses an ultrasonic diagnostic device which is configured to generate a high quality 3-dimensional image with a small amount of data. In this device, the volume data in the collection coordinates are divided along the surface defined based on a predetermined sight line direction to generate a plurality of slice data, an intermediate image corresponding to each of a plurality of sliced surfaces is calculated, and accumulation of the intermediate images is carried out so that a display image is generated.
In the cases of the above-mentioned techniques, the detection of a smooth continuation line is possible and their effectiveness is confirmed. However, it is assumed for all the above-mentioned techniques that a lacking part is estimated by using a certain method and it is interpolated by an artificial line.
To obviate the problem, the present inventors have proposed the new technique of extracting an image of an object from the CT data containing several noises and published the fundamental study on the effectiveness in the following documents:                Befu S, Tsunashima H, Arai Y: “A Study on the 3-Dimensional Model Construction Using Ortho-CT”, Institute of Electronics, Information and Communication Engineers Technical Research Report MI2000-75, 2001, pp. 145-149        Tsunashima H, Befu S, Arai Y “Stereoscopic Image Construction Method” (Japanese Patent Application No. 2000-358420), 2000        Befu S, Tsunashima H, Arai Y: “A Study in 3-Dimensional Image Processing Method for 3 DX Multi Image Micro CT”, CARS2001, 2001, pp. 665-670        Tsunashima H, Befu S, Yamada A, Arai Y: “3-Dimensional Image Construction Method In Small X-ray Calculated Tomography for Dental Use”, Med. Imag. Tech. 21:157-165, 2003.        
There is known a method for carrying out post-correction processing by choosing automatically a matrix filter which is suited for the image when applying a matrix filter as post-correction processing to the reconstructed image data in a medical image processing device. See Japanese Laid-Open Patent Application No. 07-000385.
Japanese Laid-Open Patent Application No. 09-204518 discloses a method for calculating the accumulated average of 4 neighboring pixels (up/down/right/left), or the accumulated average of 8 neighboring pixels including diagonal pixels, of the target point in the same image with respect to parallel slice data. Also disclosed is a method for calculating the accumulated average of 6 neighboring pixels of a solid body in which 4 neighboring pixels in the same image and the pixels of the same positions in the adjacent image are added, or the accumulated average of 26 neighboring pixels of a solid body in which 8 neighboring pixels in the same image and 3×pixels in the adjacent image are added.
However, the method of this document is related to the slice data correction processing, and there is no teaching in this document of calculating the integrated value of consecutive voxels in a 3-dimensional CT data without changing the 3-dimensional CT data for the correction as in the present invention. Japanese Laid-Open Patent Application No. 2002-374418 discloses a method for performing the processing corresponding to the pixel value, and performing the noise reduction processing and the sharp image processing by a single processing system.
However, the method of this document is related to the smoothing processing in which the low frequency components and the high frequency components are taken into account, and there is no teaching in this document of calculating the integrated value of consecutive voxels in a 3-dimensional CT data without changing the 3-dimensional CT data for the correction as in the present invention.